Fig 1.
Examples illustrating the relationship between generated response data and concentration-response functions under different levels of uncertainties of data.
In all figures (a)—(d), the response slope parameter β of the true concentration-response function (the solid lines) is set to 2 (hence the true EC10 is 33), and the responses are continuous. r denotes the spacing factor between adjacent test concentrations. For the case of small uncertainties, (a) and (b), the response data (the closed circles) and the concentration-response curve determined from the data (the broken line) do not deviate very much from the true concentration-response function, and estimated EC10 and the NOEC are in good accord with the true EC10 in many cases although there were still some overestimations of EC10 due to uncertainties. For the case of larger uncertainties, (c) and (d), the response data are more likely to deviate from the true concentration-response curve. In the case of (d), the large uncertainties occasionally boosted both the NOEC and EC10 beyond the true EC10.
Fig 2.
Margins of endpoints (NOEC, EC5, and EC10) related to the scale of uncertainties (α) for the case where the spacing factor is 3.
The shaded area represents the region where the margin of endpoint exceeds the TSL20. The broken line denotes the TSL10.
Fig 3.
Margins of endpoints (NOEC, EC5, and EC10) related to the scale of uncertainties (α) for the case where the spacing factor is 2.
The shaded area represents the region where the margin of endpoint exceeds the TSL20. The broken line denotes the TSL10.
Table 1.
The robustness for NOEC and EC5 or EC10.
Fig 4.
Rates of estimated endpoints (NOEC, EC5, and EC10) exceeding the predefined benchmarks among relevant simulation runs plotted against the scale of uncertainties when the spacing factor is 3.
The comparisons were made between EC10 and TSL20, between EC5 and TSL10, and between NOEC and TSL10. The results from the last comparisons did not change if TSL10 was replaced by TSL20 (data not shown).
Fig 5.
Rates of estimated endpoints (NOEC, EC5, and EC10) exceeding the predefined benchmarks among relevant simulation runs plotted against the scale of uncertainties when the spacing factor is 2.
The comparisons were made between EC10 and TSL20, between EC5 and TSL10, and between NOEC and TSL10. The results from the last comparisons did not change if TSL10 was replaced by TSL20 (data not shown).